相关论文: Invariance of Polarization Induced by Symplectomor…

We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifold to the space of sections of a Hermitian vector bundle, a…

A prequantization bundle is a negative circle bundle over a symplectic surface together with a contact form induced by a S1-invariant connection. Given a symplectically aspherical symplectic filling of a prequantization bundle satisfying…

The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…

We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the…

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…

The aim of this article is to present unifying proofs for results in geometric quantisation with real polarisations by exploring the existence of symplectic circle actions. It provides an extension of Rawnsley's results on the Kostant…

This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic…

We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…

We prove a version of Sandon's conjecture on the number of translated points of contactomorphisms for the case of prequantization bundles over certain closed monotone symplectic toric manifolds. Namely we show that any contactomorphism of…

We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction…

We re-examine quantization via branes with the goal of understanding its relation to geometric quantization. If a symplectic manifold $M$ can be quantized in geometric quantization using a polarization ${\mathcal P}$, and in brane…

Given a compact symplectic manifold $M$, with integral symplectic form, we prequantize a certain class of functions on the path space for $M$. The functions in question are induced by functions on $M$. We apply our construction to study the…

We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result:…

This survey presents some recent results by the authors and Polterovich on the topological properties of ruled symplectic manifolds. The bundle M \to P \to B that is associated with a ruled manifold has the group of Hamiltonian…

An isometric compact group action $G \times (M,g) \rightarrow (M,g)$ is called polar if there exists a closed embedded submanifold $\Sigma \subseteq M$ which meets all orbits orthogonally. Let $\Pi$ be the associated generalized Weyl group.…

We consider circle bundles over compact three-manifolds with symplectic total spaces. We show that the base of such a space must be irreducible or the product of the two-sphere with the circle. We then deduce that such a bundle admits a…

We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.

We prove uniqueness, up to diffeomorphism, of symplectically aspherical fillings of certain unit cotangent bundles, including those of higher-dimensional tori.

Let $S^1$ act on a symplectic manifold in a Hamiltonian fashion with momentum map $\Psi$. Fix a value $a$ of $\Psi$. There is a question of whether the symplectic quotient at $a$ is diffeomorphic to the orbit space of some proper Lie group…

For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the…